Non-parametric methods under cross-sectional dependence

Abstract

The possible presence of cross-sectional dependence in economic panel or cross-sectional data needs to be taken into consideration when developing econometric theory for data analysis. This thesis consists of three works that either allow for or estimate cross-sectional dependence in the disturbance terms of a regression model, each addressing
different problems, models and methods in the areas of non- and semi-parametric estimation.
Chapter 1 provides an overview of the motivations for, and contributions of, the three topics of this thesis. A review of relevant literature is given, followed by a sum-
mary of main results obtained in order to help place the present thesis in perspective. Chapter 2 develops asymptotic theory for series estimation under a general setting of
spatial dependence in regressors and error term, including cases analogous to those known as long-range dependence in the time series literature. A data-driven studentization, new to non-parametric and cross-sectional contexts, is theoretically justified, then used to develop asymptotically correct inference. Chapter 3 discusses identification and kernel estimation of a non-parametric common regression with additive individual fixed effects in panel data, with weak temporal dependence and arbitrarily strong cross-sectional dependence. An efficiency improvement is obtained by using
estimated cross-sectional covariance matrix in a manner similar to generalised least squares, achieving a Gauss-Markov type efficiency bound. Feasible optimal bandwidths and feasible optimal non-parametric regression estimation are established and asymptotically justified. Chapter 4 deals with efficiency improvement in the estimation of pure Spatial Autoregressive model. We construct a two-stage estimator, which adapts to the unknown error distribution of non-parametric form and achieves the Cramer-Rao bound of the correctly specified maximum likelihood estimator. In establishing feasibility of such adaptive estimation, we find that the gain in efficiency from adaptive estimation is typically smaller than in the relevant time series context,
but could be also greater under certain asymptotic behaviour of the weight matrix of the model.